Uniform cubic bounds for irrational values of the dilogarithm

We study explicit denominator conditions ensuring the irrationality of the dilogarithm at positive and negative rational points. We prove that Li_2(p/q) is irrational whenever q > (4e^{4}/27)p^3, and obtain an explicit, slightly smaller threshold for Li_2(−p/q). The positive argument specializes the Rhin–Viola integral family and uses a uniform estimate for a restricted prime divisor. The negative argument combines the same arithmetic construction with three adjacent integral moments and an explicit maximization. We also give finite-numerator refinements by interpolating certified partition bounds and by introducing a comparison measure with a quadratic tail. In particular, Li_2(5/q) is irrational for every integer q ≥ 418. The proof separates the established integral and determinant constructions from the parameter estimates and finite certificates used here.